SOLUTION: Could someone help me understand how to solve the problem posted...especially how the variable or unknown will be removed from the denominator. Any help would be greatly appreciate

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Question 137256: Could someone help me understand how to solve the problem posted...especially how the variable or unknown will be removed from the denominator. Any help would be greatly appreciated.
Question:
Solve the following system:
5/3a - 7 = -2/5b
7/6a - 1/10b = 3

Answer by stanbon(57967) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following system:
(5/3)a - 7 = (-2/5)b
(7/6)a - (1/10)b = 3
------------
Multiply thru the 1st equation by (1/2) to get:
(5/6)a - (7/2) = (-2/10)b
Rearrange to get:
A) (5/6)a + (2/10)b = (7/2)
Multiply 2nd equation by 2 to get:
B) (14/6)a - (2/10)b = 6
----------------------
Add equation A to equation B to solve for "a":
(19/6)a = 19/2
(1/6)a = 1/2
a = 3
-----------
Substitute that into (7/6)a - (1/10)b = 3 to solve for "b"
(7/6)3 - (1/10)b = 3
(-1/10)b = (-1/6)3
b = (-10)(-1/2)
b = 5
--------------
Final answer: a=3; b=5
================================
Cheers,
Stan H.